Simulation Using Purrr map2 for two sample ttest

### Avoid for loops with purrr
### Simulate With Purrr map & map2

require(tidyverse)

### Mean and SD from two groups ==> HRT and Placebo
### Within each group we have two measurements, HDL and LDL
d <- tibble(group = c("HRT", "Placebo"),
       MeanHDL  = c(8.1, 2.4),
       sdHDL = c(10.5, 4.3),
       MeanLDL  = c(-18.2, -2.2),
       sdLDL = c(26.5, 12.2))

d

## # A tibble: 2 x 5
##   group   MeanHDL sdHDL MeanLDL sdLDL
##   <chr>     <dbl> <dbl>   <dbl> <dbl>
## 1 HRT         8.1  10.5   -18.2  26.5
## 2 Placebo     2.4   4.3    -2.2  12.2

### For vertical lines in ggplot
vline.data <- data.frame(z = c(8.1, 2.4, -18.2, -2.2), 
                         Type = c("SimHDL", "SimHDL", "SimLDL", "SimLDL"))
vline.data

##       z   Type
## 1   8.1 SimHDL
## 2   2.4 SimHDL
## 3 -18.2 SimLDL
## 4  -2.2 SimLDL

### Simulate
dsim <- d %>% 
  mutate(SimHDL = map2(MeanHDL, sdHDL, ~ rnorm(10000, ..1, ..2)),
         SimLDL = map2(MeanLDL, sdLDL, ~ rnorm(10000, ..1, ..2))
  ) 
### purrr just enabled me to avoid writing TWO for loops
dsim

## # A tibble: 2 x 7
##   group   MeanHDL sdHDL MeanLDL sdLDL SimHDL         SimLDL        
##   <chr>     <dbl> <dbl>   <dbl> <dbl> <list>         <list>        
## 1 HRT         8.1  10.5   -18.2  26.5 <dbl [10,000]> <dbl [10,000]>
## 2 Placebo     2.4   4.3    -2.2  12.2 <dbl [10,000]> <dbl [10,000]>

head(dsim %>% 
       unnest(cols = SimHDL:SimLDL)
     )

## # A tibble: 6 x 7
##   group MeanHDL sdHDL MeanLDL sdLDL SimHDL SimLDL
##   <chr>   <dbl> <dbl>   <dbl> <dbl>  <dbl>  <dbl>
## 1 HRT       8.1  10.5   -18.2  26.5  -1.14  -8.39
## 2 HRT       8.1  10.5   -18.2  26.5  13.0  -40.9 
## 3 HRT       8.1  10.5   -18.2  26.5  17.0  -30.1 
## 4 HRT       8.1  10.5   -18.2  26.5  13.6  -13.1 
## 5 HRT       8.1  10.5   -18.2  26.5   3.14 -31.9 
## 6 HRT       8.1  10.5   -18.2  26.5  -1.75  16.2

### Make Plot
plotly::ggplotly( 
  dsim %>% 
  pivot_longer(cols = SimHDL:SimLDL,names_to = "Type", values_to = "Value") %>% 
  unnest() %>% 
  ggplot(aes(Value, fill = group, color = group)) + 
  geom_density(alpha = 0.3) +
  geom_vline(data = vline.data, aes(xintercept = z), alpha = 0.5, linetype = "longdash")+
  facet_wrap(~Type, scales = "free") +
  theme_light()
)

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References

Weiss, NA. 2005. “Introductory Statistics.” Pearson Education, Inc.

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